To solve the equation \( y^2 = 169 \), we need to find the values of \( y \) that satisfy this equation. Here's the step-by-step solution:

1. Start with the given equation:
   \[
   y^2 = 169
   \]

2. Take the square root of both sides to solve for \( y \):
   \[
   y = \pm \sqrt{169}
   \]

3. Calculate the square root of 169:
   \[
   \sqrt{169} = 13
   \]

4. Therefore, the solutions are:
   \[
   y = 13 \quad \text{or} \quad y = -13
   \]

So, the solutions to the equation \( y^2 = 169 \) are \( y = 13 \) and \( y = -13 \).

Would you like more details or have any questions about this solution?

Here are 5 related questions that expand on this information:
1. What are the solutions to the equation \( x^2 = 225 \)?
2. How would you solve the equation \( y^2 = 144 \)?
3. What are the steps to solve the equation \( z^2 = 81 \)?
4. If \( a^2 = 196 \), what are the possible values of \( a \)?
5. How do you solve \( b^2 = 100 \) and what are its solutions?

**Tip:** When solving quadratic equations like \( y^2 = k \), always remember to consider both the positive and negative roots of \( k \).

Learn how to solve the quadratic equation y^2 = 169 using the properties of square roots. This problem demonstrates key algebraic concepts, including finding both positive and negative solutions. Suitable for students in Grades 7-9.

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